# geometry

two smaller prisms have heights 2' and 10'. If the volume of the smaller prism is 32 cubic feet, find the volume of the larger prism.

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1. are we to assume that the prisms have the same base?
If so, then the volume of the larger would simply be five times the smaller , or 160 ft^3

If the two prism are similar, that is, their dimensions are in the same ratio, then their volumes are proportional to the cube of their sides

Larger/smaller = 5^3/2^3
larger/32 = 125/8
larger = 32(125/8) = 500

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2. "two similar prisms have heights 2' and 10'. If the volume of the smaller prism is 32 cubic feet, find the volume of the larger prism. "

If the prisms are similar, the volumes are proportional to the cube of the linear dimensions.

The volume of the larger prism is therefore:
V=32 ft³*(10/2)²
=4000 ft³

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